How to place a single crisp element as an alpha while sculpting?
To do this only with sculpting add the logo as the texture mask to the sculpting brush, switch Stroke method to Drag Dot and draw on the object's surface.



The texture defines a pattern according to which the brush is painting. Drag Dot stroke method will make brush draw only one dab preserving pattern of the texture.

Note that depending on the case you might need to continue sculpting with other stroke methods (use E to change) to bulge the logo out of the surface as desired. And obviously this model will be highpoly which is better to retopologize using certain methods.